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arXiv · 2006.01920

Multivariate volume, Ehrhart, and $h^*$-polynomials of polytropes

Marie-Charlotte Brandenburg·Sophia Elia·Leon Zhang
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Abstract

The univariate Ehrhart and $h^*$-polynomials of lattice polytopes have been widely studied. We describe methods from toric geometry for computing multivariate versions of volume, Ehrhart and $h^*$-polynomials of lattice polytropes, which are both tropically and classically convex. These algorithms are applied to all polytropes of dimensions 2,3 and 4, yielding a large class of integer polynomials. We give a complete combinatorial description of the coefficients of volume polynomials of 3-dimensional polytropes in terms of regular central subdivisions of the fundamental polytope. Finally, we provide a partial characterization of the analogous coefficients in dimension 4.

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Marie-Charlotte Brandenburg, Sophia Elia, Leon Zhang. 2020-06-02. Multivariate volume, Ehrhart, and $h^*$-polynomials of polytropes. https://doi.org/10.1016/j.jsc.2022.04.011

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